The basic layout of your plan is very good. Clearly you have given this some thought. It doesn't show the martial arts work, so I'll assume you aren't doing it at the moment.
If you can't run a mile at this point, though, then perhaps you should postpone the HIIT work for a while. Building a minimal base of cardio fitness first is much more likely to let you adapt successfully to the routine.
If you want to push things along on the fast side:
Tuesday - pretty much as you describe it; effort level - conversation would be somewhat interrupted by the need to breath, but not badly so; start out keeping the distance short (something you can manage pretty easily) and add no more than 10% per week.
Thursday - Push the tempo somewhat harder than Tues, so conversation is inconvenient but still barely manageable - no harder than this, though. Again, keep the duration easily doable at first and add gradually. This day should always be shorter (60-75% of the total time) than Tuesday.
This should serve you well for at least 6 weeks. Then you might consider making Thursday interval day. Even then (and for a while at least) keep the work periods of the intervals longish - 90 sec to 2 minutes - and the effort level at what would be described as "hard", something you could probably do continuously about 15 minutes if you tried but likely not a half hour. Start out doing no more than 4 of these work periods per session and add them gradually until you are doing perhaps 6-8.
As is often the case with
resistance exercise, many people try to go at aerobic work too hard at first and never work out a plan they can live with. You know better than I what your own tendencies are, but it sounds like you might be one of these people.The adaptations required take weeks to develop so have some patience.
As for loss of muscle, every body is different but I'll stick my neck out and suggest you have nothing to worry about here. Your eating strategy is sound and should work fine for you.
Finally, about 3 million years of evolution makes running one of THE distinguishing capabilities of humanity, but if running really doesn't agree with you then please consider one of the many alternative forms of
aerobic exercise. My experience is that people benefit greatly from finding something they enjoy. Life is too short to compromise on this point.
Be well,
Carl